Parametric Conics

Sketch the curve of x(t) = 2t + 1 and y(t) = t² + 2. Hint: Make a three column chart but plot only x and y.

• A

• B

• C

• D

Write the pair of parametric equations in rectangular form then determine the shape of the graph.  
x = 3 cos ⊖  and y = 5 sin ⊖

• ellipse

• circle

• hyperbola

• parabola

Write x = 2t and y = t² + 3 in rectangular form . Solve the x equation for t and then substitute that into the t of the y equation.

• y = 4x² + 3

• y = ¼ x² + 3

• y = 4t² + 12

• y = (x - 2)² + 3

What curve do the parametric equations make? What is the direction of motion? x= 1+3cost

y= -2+4sint

• Circle. Counterclockwise.

• Circle. Clockwise.

• Ellipse. Counterclockwise.

• Ellipse. Clockwise.

Write the rectangular equation for the following parametric equations.

Write in rectangular form.

x = 4cos θ

y = 4sin θ

• x + y = 16

What is the center and radius of the curve:

x= -1 + 9cost

y= 2 + 9sint

• (-1,2) , r=3

• (-1,2) ,  r=9

• (1,-2) ,  r=3

• (1,-2) ,  r=9

• Vertical Ellipse
• Vertical Hyperbola
• Horizontal Ellipse
• Horizontal Hyperbola

Identify the center and the length of a and b.

• C: (0,0)  a= 25, b=4

• C: (0,0)  a= 4, b=25

• C: (0,0)  a= 2, b=5

• C: (0,0)  a= 5, b=2